Creating descriptors for trajectories has many applications in robotics/human motion analysis and video copy detection. Here, we propose a novel descriptor for 2D trajectories: Histogram of Oriented Displacements (HOD). Each displacement in the trajectory votes with its length in a histogram of orientation angles. 3D trajectories are described by the HOD of their three projections. We use HOD to describe the 3D trajectories of body joints to recognize human actions, which is a challenging machine vision task, with applications in human-robot/machine interaction, interactive entertainment, multimedia information retrieval, and surveillance. The descriptor is fixed-length, scale-invariant and speed-invariant. Experiments on MSR-Action3D and HDM05 datasets show that the descriptor outperforms the state-of-the-art when using off-the-shelf classification tools.